SOLVING CRYSTAL-STRUCTURES WITH THE SYMMETRY MINIMUM FUNCTION

Unravelling the Patterson function (the auto-correlation function of t he crystal structure) (A.L. Patterson, Phys. Rev. 46 (1934) 372) can b e the only way of solving crystal structures from neutron and incomple te diffraction data (e.g. powder data) when direct methods for phase d etermination fail. The negative scattering lengths of certain isotopes and the systematic loss of information caused by incomplete diffracti on data invalidate the underlying statistical assumptions made in dire ct methods. In contrast, the Patterson function depends solely on the quality of the available diffraction data. Simpson et al. (P.G. Simpso n et al., Acta Crystallogr. 18 (1965) 169) showed that solving a cryst al structure with a particular superposition of origin-shifted Patters on functions, the symmetry minimum function, is advantageous over usin g the Patterson function alone, for single-crystal X-ray data. This pa per describes the extension of the Patterson superposition approach to neutron data and powder data by (a) actively using the negative regio ns in the Patterson map caused by negative scattering lengths and (b) using maximum entropy Patterson maps (W.I.F. David, Nature 346 (1990) 731). Furthermore, prior chemical knowledge such as bond lengths and a ngles from known fragments have been included. Two successful structur e solutions of a known and a previously unknown structure (M. Hofmann, J. Solid State Chem., in press) illustrate the potential of this new development.